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Mathematical Physics

arXiv:1812.08923 (math-ph)
[Submitted on 21 Dec 2018 (v1), last revised 18 Jun 2019 (this version, v3)]

Title:Algebraic entropy of a multi-term recurrence of the Hietarinta-Viallet type

Authors:Ryo Kamiya, Masataka Kanki, Takafumi Mase, Tetsuji Tokihiro
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Abstract:We introduce a family of extensions of the Hietarinta-Viallet equation to a multi-term recurrence relation via a reduction from the coprimeness-preserving extension to the discrete KdV equation. The recurrence satisfies the irreducibility and the coprimeness property although it is nonintegrable in terms of an exponential degree growth. We derive the algebraic entropy of the recurrence by an elementary method of calculating the degree growth. The result includes the entropy of the original Hietarinta-Viallet equation.
Comments: 24 pages, To appear in RIMS Kokyuroku Bessatsu
Subjects: Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI)
MSC classes: 37K10, 37K60
Cite as: arXiv:1812.08923 [math-ph]
  (or arXiv:1812.08923v3 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.1812.08923
Journal reference: RIMS Kokyuroku Bessatsu B78 (2020), 121--153

Submission history

From: Masataka Kanki [view email]
[v1] Fri, 21 Dec 2018 03:05:37 UTC (21 KB)
[v2] Sat, 18 May 2019 07:02:11 UTC (23 KB)
[v3] Tue, 18 Jun 2019 10:37:38 UTC (23 KB)
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